{"title":"基于香农小波的密闭原子和离子托马斯-费米模型近似方案","authors":"Sharda Kumari, Pratik Majhi, M. M. Panja","doi":"10.1134/s0965542524700350","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent <span>\\(n\\)</span> in the desired order of accuracy (<span>\\(O{{(10}^{{ - n}}})\\)</span>) with the resolution <span>\\(J\\)</span>, the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions\",\"authors\":\"Sharda Kumari, Pratik Majhi, M. M. Panja\",\"doi\":\"10.1134/s0965542524700350\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent <span>\\\\(n\\\\)</span> in the desired order of accuracy (<span>\\\\(O{{(10}^{{ - n}}})\\\\)</span>) with the resolution <span>\\\\(J\\\\)</span>, the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.</p>\",\"PeriodicalId\":55230,\"journal\":{\"name\":\"Computational Mathematics and Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0965542524700350\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700350","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions
Abstract
An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent \(n\) in the desired order of accuracy (\(O{{(10}^{{ - n}}})\)) with the resolution \(J\), the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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